Regret Minimization in Partially Observable Linear Quadratic Control

We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of O(T^(2/3)) for ExpCommit, where T is the time horizon of the problem

Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems

We study the problem of adaptive control in partially observable linear dynamical systems. We propose a novel algorithm, adaptive control online learning algorithm (AdaptOn), which efficiently explores the environment, estimates the system dynamics episodically and exploits these estimates to design effective controllers to minimize the cumulative costs. Through interaction with the environment, AdaptOn deploys online convex optimization to optimize the controller while simultaneously learning the system dynamics to improve the accuracy of controller updates. We show that when the cost functions are strongly convex, after T times step of agent-environment interaction, AdaptOn achieves regret upper bound of polylog(T). To the best of our knowledge, AdaptOn is the first algorithm which achieves polylog(T) regret in adaptive control of unknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control

Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LqgOpt and prove the regret upper bound of O(√T) for adaptive control of linear quadratic Gaussian (LQG) systems, where T is the time horizon of the problem

Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LqgOpt and prove the regret upper bound of O(√T) for adaptive control of linear quadratic Gaussian (LQG) systems, where T is the time horizon of the problem

Explore More and Improve Regret in Linear Quadratic Regulators

Stabilizing the unknown dynamics of a control system and minimizing regret in control of an unknown system are among the main goals in control theory and reinforcement learning. In this work, we pursue both these goals for adaptive control of linear quadratic regulators (LQR). Prior works accomplish either one of these goals at the cost of the other one. The algorithms that are guaranteed to find a stabilizing controller suffer from high regret, whereas algorithms that focus on achieving low regret assume the presence of a stabilizing controller at the early stages of agent-environment interaction. In the absence of such a stabilizing controller, at the early stages, the lack of reasonable model estimates needed for (i) strategic exploration and (ii) design of controllers that stabilize the system, results in regret that scales exponentially in the problem dimensions. We propose a framework for adaptive control that exploits the characteristics of linear dynamical systems and deploys additional exploration in the early stages of agent-environment interaction to guarantee sooner design of stabilizing controllers. We show that for the classes of controllable and stabilizable LQRs, where the latter is a generalization of prior work, these methods achieve $\tilde{\mathcal{O}}(\sqrt{T})$ regret with a polynomial dependence in the problem dimensions

Explore More and Improve Regret in Linear Quadratic Regulators

Stabilizing the unknown dynamics of a control system and minimizing regret in control of an unknown system are among the main goals in control theory and reinforcement learning. In this work, we pursue both these goals for adaptive control of linear quadratic regulators (LQR). Prior works accomplish either one of these goals at the cost of the other one. The algorithms that are guaranteed to find a stabilizing controller suffer from high regret, whereas algorithms that focus on achieving low regret assume the presence of a stabilizing controller at the early stages of agent-environment interaction. In the absence of such a stabilizing controller, at the early stages, the lack of reasonable model estimates needed for (i) strategic exploration and (ii) design of controllers that stabilize the system, results in regret that scales exponentially in the problem dimensions. We propose a framework for adaptive control that exploits the characteristics of linear dynamical systems and deploys additional exploration in the early stages of agent-environment interaction to guarantee sooner design of stabilizing controllers. We show that for the classes of controllable and stabilizable LQRs, where the latter is a generalization of prior work, these methods achieve O(√T) regret with a polynomial dependence in the problem dimensions